Magnetic resonance imaging (MRI) includes techniques for capturing data related to the internal structure of an object of interest, for example, by non-invasively obtaining images of internal structure of the human body, and has been widely used as a diagnostic tool in the medical community. MRI exploits the nuclear magnetic resonance (NMR) phenomenon to distinguish different structures, phenomena or characteristics of an object of interest. For example, in biological subjects, MRI may be employed to distinguish between various tissues, organs, anatomical anomalies (e.g., tumors), and/or to image diffusion, blood flow, blood perfusion, etc.
In general, MRI operates by manipulating spin characteristics of subject material. MRI techniques include aligning the spin characteristics of nuclei of the material being imaged using a generally homogeneous magnetic field and perturbing the magnetic field with a sequence of radio frequency (RF) pulses. To invoke the NMR phenomenon, one or more resonant coils may be provided proximate an object positioned within the magnetic field. The RF coils are adapted to generate RF pulses, generally in the form of RF pulse sequences adapted for a particular MRI application, to excite the nuclei and cause the spin to process about a different axis (e.g., about an axis in the direction of the applied RF pulses). When an RF pulse subsides, spins gradually realign with the magnetic field, releasing energy that can be measured to capture NMR data about the internal structure of the object.
Measuring water diffusion with magnetic resonance diffusion-weighted imaging (MR-DWI) enables probing tissue at a length scale much smaller than the image spatial resolution. This has enabled non-invasive investigation and characterization of the white matter architecture and microstructure in the brain. In particular DWI enables investigation of the brain microstructure by probing natural barriers to diffusion in tissues. Diffusion in white matter fascicles has been observed to be highly anisotropic, with primary orientation of the diffusion corresponding to the orientation of the fascicle. The underlying microstructure that gives rise to this anisotropy has been investigated. Diffusion tensor imaging (DTI) was proposed to describe the three-dimensional nature of anisotropic diffusion. Assuming homogeneous Gaussian diffusion within each voxel, DTI describes the magnitude and orientation of water molecule diffusion with a second-order tensor estimated from diffusion measurements in several directions. More precisely, DTI relates the measured diffusion-weighted signal Sk, along a gradient direction gk to the non-attenuated signal S0 via the Stejskal-Tanner equation:sk(D)=S0e−TE/T2e−γ2δ2(Δ−δ/3)gkTDgk,  (1)
where TE is the echo time, T2 is the T2 relaxation time of the tissue, γ is the gyromagnetic ratio, δ and Δ are the diffusion sensitizing pulse gradients duration and time separation, and D is the 3×3 diffusion tensor.
The applied b-value defined by bk=γ2δ2 (Δ−δ/3)Gk2, which depends on the gradient strength Gk2=∥gk∥2, has been introduced to simplify the notations in equation (1) and describes the diffusion sensitization strength. The nominal b-value bnominal=γ2δ2 (Δ−δ/3) describes the b-value for the unit-norm gradients. The term e−TE/T2 is generally considered constant across all gradients and omitted. However, and importantly, this term highlights how the signal amplitude Sk(D) decreases exponentially for increasing TE.
DTI and its underlying mono-exponential signal attenuation assumption are generally considered to satisfactorily represent single fascicles when imaging with b-values lower than 3000 s/mm2, which is frequently the case in clinical settings. Non-monoexponential behavior of the signal at a voxel in this b-value range can arise from cerebral spinal fluid (CSF) partial voluming, mixtures of fascicles present in the voxel, and other sources. The diffusion tensor enables representation of the orientation of a single fascicle, as well as the characterization of the diffusion process. Tensor parameters such as the fractional anisotropy (FA), the mean diffusivity (MD), the axial diffusivity (AD), and the radial diffusivity (RD) can be computed, and have been shown to provide valuable information that reflects changes in the white matter due to development, disease and degeneration. DTI requires relatively short acquisition times and has been successfully employed in clinical studies.
DTI has been shown to be a poor parametric model for representing the diffusion signal arising at voxels that encompass multiple fascicles with heterogeneous orientation such as fascicle crossing, kissing or fanning. Several approaches have been investigated to overcome this fundamental limitation, which involve various diffusion signal sampling schemes and ways to analyze the diffusion signal as detailed below.
Cartesian sampling and spherical sampling are two q-space sampling strategies that have been used for complex fiber structure assessment. Cartesian sampling is used by diffusion spectrum imaging (DSI). Spherical sampling as employed in high angular resolution imaging (HARDI) techniques reduces the imaging time and requires imaging gradients with moderate intensity. Several HARDI-based techniques have been proposed, as discussed in further detail below. Single-shell HARDI acquisitions with a single non-zero b-value have been considered to image a sphere of constant radius in q-space. Multiple-shell HARDI acquisitions that enable the acquisition of multiple non-zero b-values by combining in a single acquisition, the sampling of multiple shells of different radius in q-space, have also been proposed.
Other sampling techniques have been proposed for reasons other than assessing complex fiber structures. For example, sampling using the tetrahedral √{square root over (3)}-norm gradients has been employed to measure the apparent diffusion coefficient (ADC) from four diffusion measurements. Because bk=bnominalGk2, this technique enables imaging at higher b-values than the nominal b-value without modifying the timing parameters δ and Δ, but by using gradients with norm greater than one. It provides the optimal minimum achievable TE for the corresponding applied b-value, leading to a better SNR and potentially to lower eddy current distortion because the diffusion gradient pulses can be shortened. Using the same concept, the six hexahedral √{square root over (2)}-norm gradients may be used to estimate a diffusion tensor from seven measurements. Furthermore, in (CUbe Rays to Vertices and Edges) CURVE-ball, a spherical sampling and the hexahedral and tetrahedral gradients are combined to perform the estimation of a single-tensor model at three different diffusion scales bnominal, 2bnominal, and 3bnominal.
Several approaches have been investigated to analyze the diffusion signal and represent multiple white-matter fascicles with complex geometry. Both parametric (model-based) and non-parametric (model-free) approaches have been proposed. Generally, these models focus on estimating either (1) the diffusion displacement probability density function (diffusion PDF), (2) the diffusion orientation distribution function (dODF) which is the angular profile of the diffusion PDF or (3) the fiber orientation distribution function (fODF), also known as the fiber orientation density (FOD) and which is of central interest for tractography.
Model-free approaches include diffusion spectrum imaging (DSI). In this technique, the diffusion PDF is directly estimated from the inverse Fourier transform of the measured signal, requiring a very high number of measurements to satisfy the Nyquist condition. Q-ball imaging (QBI) estimates an approximate non-parametric angular profile of the diffusion PDF without actually computing the diffusion PDF, by using the Funk-Radon transform. Fast and robust analytical QBI estimation procedures have been proposed. QBI results in the estimation of an approximated dODF related to the true dODF by modulation with a zero-order Bessel function. This leads to a spectral broadening of the diffusion peaks of individual fascicles at moderate b-values accessible on a clinical scanner, perturbing the FOD reconstruction necessary for carrying out tractography. Mixing of individual tracts in a voxel leads to local maxima that does not coincide with the true fascicle orientation, leading to a relatively low fidelity representation. To avoid the usual Q-Ball approximation, an Exact Q-Ball Imaging (EQBI), which derives a direct relationship between the dODF and the diffusion data has been proposed. EQBI enables the estimation of the exact dODF under the assumption of a Gaussian profile.
Q-space approaches such as DSI, QBI, or EQBI are limited by at least three error sources. These techniques are based on the narrow pulse approximation assumption, considering that molecules do not diffuse during the application of the diffusion sensitizing gradients. The gradient pulses are then modeled by a Dirac shape which is not practically feasible, especially on clinical systems. In practice, in clinical settings, the diffusion-encoding gradient duration δ is typically of the same order of magnitude as the time offset Δ between encoding gradients (Δ/δ≈1) to minimize T2 decay and to obtain better SNR, which is a very poor approximation of a Dirac shape. Additionally, since the imaging time has to be finite, only a finite region in q-space is imaged using these techniques. This has been shown to lead to a blurred propagator with decreased contrast and angular resolution. Also, these techniques are limited by the need to truncate the Fourier representation which is required to numerically compute the infinite series involved in the Fourier transformation, leading to quantization artifacts.
In contrast, parametric models describe a predetermined model of diffusion rather than an arbitrary one. They potentially require a smaller number of images to be acquired, leading to a reduced acquisition time. Several model-based approaches have been investigated. Among them, generalized diffusion tensor imaging (GDTI) models the white-matter fascicles with higher-order tensors; spherical deconvolution (SD) directly estimates the FOD instead of the dODF and has a better angular resolution; and diffusion orientation transform (DOT) employs a model-based q-space modeling based on the assumption of a monoexponential decay of the signal attenuation.